Question

Calcule o nono termo da P.G (81, 27, 9, ... )

Answer 1

$\displaystyle \mathsf{a_1 = 81}\\ \displaystyle \mathsf{q = \frac{1}{3}}\\ \displaystyle \mathsf{n = 9}\\ \displaystyle \mathsf{a_9 = ?}$

$\displaystyle \mathsf{a_n = a_1.q^{n-1}}\\ \displaystyle \mathsf{a_9 = 81.\frac{1}{3}^{9-1}}\\ \displaystyle \mathsf{a_9 = 3^4.3^{-8}}\\ \displaystyle \mathsf{a_9 = 3^{-4}}\\ \displaystyle \mathsf{a_9 = \frac{1}{81}}$

Answer 2

an = a1 . q elevado a n-1
a9= 81 . (1/3) elevado a 9-1
a9= 3⁴ . (1/3) elevado a 8
a9= 3⁴ . (3) elevado -8
a9= 3 elevado a -4
a9= 1/81